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Inspired by the theory of hyperbolic polynomials and Hodge theory, we develop the theory of Lorentzian polynomials on cones. This notion captures the Hodge-Riemann relations of degree zero and one. Motivated by fundamental properties of…
Fluid-based locomotion at low Reynolds number is subject to the constraints of the scallop theorem, which dictate that body kinematics identical under a time-reversal symmetry (in particular, those with a single degree of freedom) cannot…
Uniform bounds on sketched inner products of vectors or matrices underpin several important computational and statistical results in machine learning and randomized algorithms, including the Johnson-Lindenstrauss (J-L) lemma, the Restricted…
A rational pseudo-rotation $f$ of the torus is a homeomorphism homotopic to the identity with a rotation set consisting of a single vector $v$ of rational coordinates. We give a classification for rational pseudo-rotations with an invariant…
We count primitive lattices of rank $d$ inside $\mathbb{Z}^{n}$ as their covolume tends to infinity, with respect to certain parameters of such lattices. These parameters include, for example, the subsapce that a lattice spans, namely its…
We extend the Razumov-Stroganov conjecture relating the groundstate of the O(1) spin chain to alternating sign matrices, by relating the groundstate of the monodromy matrix of the O(1) model to the so-called refined alternating sign…
We derive a local limit theorem for normal, moderate, and large deviations for symmetric simple random walk on the square lattice in dimensions one and two that is an improvement of existing results for points that are particularly distant…
This talk covers recent theoretical progress in exclusive semileptonic rare B-decays at low hadronic recoil. The efficient parametric suppression of the 1/mb corrections in this region provides opportunities to probe the Standard Model and…
In this paper we motivate some new directions of research regarding the lattice width of convex bodies. We show that convex bodies of sufficiently large width contain a unimodular copy of a standard simplex. This implies that every lattice…
We study rigidity problems for Riemannian and semi-Riemannian manifolds with metrics of low regularity. Specifically, we prove a version of the Cheeger-Gromoll splitting theorem \cite{CheegerGromoll72splitting} for Riemannian metrics and…
We study ordinary solitons and gap solitons (GSs) in the effectively one-dimensional Gross-Pitaevskii equation, with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of the…
The model of a bicycle is a unit segment AB that can move in the plane so that it remains tangent to the trajectory of point A (the rear wheel is fixed on the bicycle frame); the same model describes the hatchet planimeter. The trajectory…
Given a convex function $\varphi$ and two hermitian matrices $A$ and $B$, Lewin and Sabin study in [M. Lewin, J. Sabin, {\it A Family of Monotone Quantum Relative Entropies}, Lett. Math. Phys. \textbf{104} (2014), 691-705.] the relative…
We conjecture that the relative Gromov-Witten potentials of elliptic fibrations are (cycle-valued) lattice quasi-Jacobi forms and satisfy a holomorphic anomaly equation. We prove the conjecture for the rational elliptic surface in all…
The k-monotone classes of densities defined on (0, \infty) have been known in the mathematical literature but were for the first time considered from a statistical point of view by Balabdaoui and Wellner (2007, 2010). In these works, the…
Inspired by the methods of Voisin, the first two authors recently proved that one could read off the gonality of a curve C from the syzygies of its ideal in any one embedding of sufficiently large degree. This was deduced from from a…
Completing a strategy of Gou\"ezel and Lalley, we prove a local limit theorem for the random walk generated by any symmetric finitely supported probability measure on a non-elementary Gromov-hyperbolic group: denoting by $R$ the inverse of…
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to…
Lorentz-violating theories of gravity typically contain constrained vector fields. We show that the lowest-order coupling of such vectors to $\mathrm{U}(1)$-symmetric scalars can naturally give rise to baryogenesis in a manner akin to the…
There are important conjectures about logarithmic conformal field theories (LCFT), which are constructed as kernel of screening operators acting on the vertex algebra of the rescaled root lattice of a finite-dimensional semisimple complex…